If you have unlimited data over 3G so that cost is no option, which is more power efficient?
Using the WiFi or 3G connection for data usage?
Extending battery life being the goal
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It depends on several things
As Matthew Read mentions, the hardware, your location, and the other fiddly bits about actual communication are important to the discussion. But, you also need to consider what you're doing with the phone.
Are you retrieving largish amounts of data often? If so, Wifi may be less drain on the battery by letting you finish sooner - remember the screen drains power while you're waiting for 3G to finish what WiFi may have finished much sooner. (But that depends on what brightness level you have your phone set to.)
In short, set your phone up the way you like to use it, in the place you like to use it. Then run the best test you can to see which uses more battery. Keep everything as much the same during the tests as possible. (Know exactly which apps are running, plan what data to use, and time how long you use the data after it's retrieved.)
I never really did a precise comparative test but it is clear that wifi uses way less power than the 3G data connection. So I would recommend to use wifi whenever possible if the goal is to extend battery life.
The only exception I would see is if you often use the phone but for a very short moment at a time, the delay it takes for the wifi to connect can be a hassle. In this case only I would deactivate the wifi.
I can't remember where I read it but I read that 3G will use more power when transfering data but wifi will use more when idling. I tend to keep wifi on, but if I'm running low on power I'll turn it off to avoid the power requirements of scanning for new networks. Also as others have posted, 2G will use less power than both unless you're downloading large files!
Try with your particular phone. Maybe download a large file and see how much the battery drains, then repeat for the other data type. Factors include how many cell towers are nearby, how many packets your WiFi drops, your specific chipset and radio hardware, software drivers, and the like.
While it was true in previous generations of phones that Wifi used more power in idle, it's less true in later generations(think HTC Desire Z and up), with latests wifi chips.
If you are using data, Wifi is then preferable: uses less power, and can have more bandwidth and less latencies depending on the provider… Although public hotspots tend to match latencies and bandwidth of 3G networks… (on purpose?)
The main battery drain happens when there is actual data transfer. Since the speed of WiFi is much faster compared to 3G, it uses less power to download the same amount of data since it finishes downloading faster.
Also the transmuting power of WiFi is usually smaller than this of a 3G radio since the access point is much closer and the signal much stronger than the usual 3G tower. They tend to be less dense than 2G towers and the phone will need to transmit with more power in order to keep reasonable signal strength with 3G.
I can confirm the experiences of 3G using more power than wifi, and I do believe it is, in fact, stated by Google somewhere in the Android FAQ.
The technical reason probably has to do with the fact that there is much more negotiation going on for 3G, where there could be many radio towers involved, and where they will actually instruct the phone to beef up transmission power if needed. Also, it goes without saying, that there ought to be a difference considering wifi has a coverage area limited to some 20-100 meters depending on equipment and obstacles; whereas 3G operates over a much longer distance up around several Km.
Both operate within a fairly similar frequency band of 1.9GHz to 2.4GHz. In general, the higher the frequency, the more data can be transferred but it also takes more power to get a signal through obstacles. This is also why it's sometimes recommended to turn off 3G (rely on only 2G) in order to conserve battery, since 2G networks usually operate at a much lower frequency band around 800-1000MHz.
this is subjective my friends.. no exact answer. is definite answer.
scenario 1 - you have a good wifi reception - phone dont have to try hard to fetch network, so battery life is longer. but if wifi is tough to connect then offcourse the phone needs to work hard.. so battery drain quicker.
scenario 2 - you using data network, but in bad reception area then it would have same affect on your battery - drained faster..
in the end, depend on your area's connection in order to have longer battery life.. who knows which connection is the best in tht particular area. just simple logic. no technical wonders can save your battery life i say..
About some weeks ago I have bought one Xiaomi Redmi 4x (5", octa, Dual Sim, Dual StandBy, with 4G primary SIM and 3G secondary SIM, 3GB/32GB) and two Xiaomi Redmi Note 4x (5.5", deca, Dual Sim, Dual StandBy, with 4G primary SIM and 3G secondary SIM, 4GB/64GB). The battery on all three is 4100 mAh.
Because of some posts on another forum that state that "the battery is bad" on these phones, I have tried to execute some tests.
It is not important that I think the battery is very good, but about the disscution above I think is important to say that when I use the only the data connection (4G - Band 1 FDD or Band 38 TDD=my provider) the slope of the power drain is more steep than when it is used only the WiFi either on 2.4 GHz (Redmi 4x) or 5 GHz Redmi Notte 4x).